JPS59127006A - Fresnel zone plate - Google Patents

Fresnel zone plate

Info

Publication number
JPS59127006A
JPS59127006A JP264883A JP264883A JPS59127006A JP S59127006 A JPS59127006 A JP S59127006A JP 264883 A JP264883 A JP 264883A JP 264883 A JP264883 A JP 264883A JP S59127006 A JPS59127006 A JP S59127006A
Authority
JP
Japan
Prior art keywords
fresnel zone
refractive index
plate
transparent
concave
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
JP264883A
Other languages
Japanese (ja)
Other versions
JPS6311641B2 (en
Inventor
Kenji Tatsumi
辰巳　賢二
Riichi Saeki
佐伯　利一
Toshio Takei
竹居　敏夫
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Mitsubishi Electric Corp
Original Assignee
Mitsubishi Electric Corp
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Mitsubishi Electric Corp filed Critical Mitsubishi Electric Corp
Priority to JP264883A priority Critical patent/JPS59127006A/en
Publication of JPS59127006A publication Critical patent/JPS59127006A/en
Publication of JPS6311641B2 publication Critical patent/JPS6311641B2/ja
Granted legal-status Critical Current

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Classifications

    • G—PHYSICS
    • G02—OPTICS
    • G02B—OPTICAL ELEMENTS, SYSTEMS OR APPARATUS
    • G02B5/00—Optical elements other than lenses
    • G02B5/18—Diffraction gratings
    • G02B5/1876—Diffractive Fresnel lenses; Zone plates; Kinoforms

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  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Optics & Photonics (AREA)
  • Diffracting Gratings Or Hologram Optical Elements (AREA)
  • Lenses (AREA)
  • Optical Couplings Of Light Guides (AREA)

Abstract

PURPOSE:To eliminate a difference in sphericity and to reduce coma-aberration by regarding the concave surface side of a plano-concave lens as an incident surface where parallel light strikes, forming a Fresnel zone on the plane side, and specifying the radii of rings and the thickness, refractive index, radius of curvature, etc., of said plano-concave lens. CONSTITUTION:A Fresnel zone plate 3 uses the concave surface of the plano- concave lens 19 as the incident surface where the parallel light strikes and has the Fresnel zone 2 on the plane side; and simultaneous equations I -VI hold for radii of rings, and the refractive index, thickness, and radius of curvature of the plano-concave lens 19 are so determined that the evaluated amount of residual coma-aberration is reduced, thereby reducing the spot diameter of a diffraction limit and coma-aberration in a transparent material 8 which has a >=1 refractive index. Thus, the radii rk of rings of the Fresnel zone, thickness d1 and refractive index n1 of the concave transparent plate, and thickness d2 and refractive index n2 of the parallel transparent plate are determined, and consequently the coma- aberration of projected light is eliminated even if the incident parallel light slants to an optical axis, so that a sharp spot is obtained at a convergence point 7.

Description

【発明の詳細な説明】 この発明は、空気中よシ屈折率が１以上の透明な物質中
の１点に平行光を集光させ、かつコマ収差のないフレネ
ルゾーンプレートに関するものである。DETAILED DESCRIPTION OF THE INVENTION The present invention relates to a Fresnel zone plate that focuses parallel light on a point in a transparent material having a refractive index of 1 or more in air and is free from coma aberration.

従来のこの櫛フレネルゾーンプレートはその輪帯の半径
ｒｋが第１式 で与えられる値をもち、平行平板のガラス板の庁面のみ
にフレネルゾーンが形成される構成罠なっていた。第１
弐において、λは波長、ｆは焦点距７１、に＝１．ａし
・・である。このフレネルゾーンプレートの作用を第１
図に示す。第１図において。This conventional comb Fresnel zone plate has a radius rk of its ring zone given by the first equation, and has a trap structure in which a Fresnel zone is formed only on the surface of the parallel flat glass plate. 1st
2, λ is the wavelength, f is the focal length 71, and =1. It is... The first function of this Fresnel zone plate is
As shown in the figure. In FIG.

は）はガラス板、（２）はフレネルゾーン、１３）はフ
レネルゾーンプレー）、１４１は光軸、（５）は入射平
行光。) is the glass plate, (2) is the Fresnel zone, 13) is the Fresnel zone play), 141 is the optical axis, and (5) is the incident parallel light.

（６）は出射光、（７）は集光点である。このような構
成の７レネルゾーングレート（３）に光軸（４）に平行
な入射光が入射すると、入射平行光（５）はフレネルゾ
ーン（２）の半径ｆｋのところで回折され、集光点（７
）に向う出射光線（６）Ｋ変換され、他の入射光線も同
様に集光点（７）に向う出射光線（６）に変換される。(6) is the emitted light, and (7) is the condensing point. When incident light parallel to the optical axis (4) enters the 7-Resnel zone grating (3) with such a configuration, the incident parallel light (5) is diffracted at the radius fk of the Fresnel zone (2) and focused. Point (7
), and the other incident light rays are similarly converted into output light rays (6) heading towards the focal point (7).

この場合には集光点（７）では集差を生じることなく回
折限界のスポットサイズをもつ集光光が得られる。In this case, condensed light having a diffraction-limited spot size can be obtained at the condensing point (7) without causing any convergence.

この状ＤＩＩＣおけるスポットダイアグラムを第２＃１
！Ｊ−に示す。The spot diagram in this state DIIC is #2 #1.
! Shown in J-.

次に、オ山式で与えられる輪帯をもつフレネルゾーンプ
レートを用いて、空気中よシ屈折率ｎ２＞１の透明な物
質中へ平行光を集光させる場合には。Next, when collimated light is focused in air into a transparent material with a refractive index n2>1 using a Fresnel zone plate having annular zones given by the Oyama equation.

空気と上記透明・物質との境界で屈折が起きるため球面
収差が生じ、集光点でのスポット径が回折限界による値
よシも大きくなシ、７ヤーグに集光することができなく
なる。この状態を示したものが第３図である。第３図に
おいて、１３）は第１図で説明した輪帯半径が第１式で
与えられるフレネルゾーングレー）、＋８１は屈折率ｎ
２〉１の透明物質、（９）は上記透明物質と空気との境
界である。プレネルゾーンプレート（３）で回折された
出射光（６）は焦点Ｃ１ｏ＋に向う光線となるか、境界
（９）で屈折されるため。Spherical aberration occurs because refraction occurs at the boundary between air and the above-mentioned transparent substance, and the spot diameter at the focal point is larger than the value due to the diffraction limit, making it impossible to focus the light into a 7-year radius. FIG. 3 shows this state. In Figure 3, 13) is the Fresnel zone gray whose annular radius explained in Figure 1 is given by the first equation), +81 is the refractive index n
2>Transparent substance in 1, (9) is the boundary between the transparent substance and air. This is because the outgoing light (6) diffracted by the Plenel zone plate (3) becomes a light beam heading toward the focal point C1o+ or is refracted at the boundary (9).

この面における屈折の法則に従った方向に変えられ、光
軸（４）とは焦点叫とは異なる位置で交わる。The direction is changed according to the law of refraction in this plane, and it intersects with the optical axis (4) at a position different from the focal point.

他の光線も同様にして境界（９）で屈折され集光点（７
）の近停で光軸と交わる。この先軸と交わる位置は各光
線によル異なるため１点では交からす、集光点（７）に
おける像はボケ、そのスポット径は回折限界による値よ
シも大きくなる。これを第４図に示す。Other light rays are similarly refracted at the boundary (9) and focused at the focal point (7).
) intersects the optical axis at a nearby stop. Since the position at which the rays intersect with the front axis differs for each ray, they do not intersect at one point, the image at the condensing point (7) is blurred, and the spot diameter is larger than the value due to the diffraction limit. This is shown in FIG.

また、第１図で示したフレネルゾーンプレー（３）Ｋ上
記光軸＋４１に対して傾きをもつ平行光ｕ１１を入射し
た場合には、コマ収差が生じ、集光点でのスポット径が
回折限界による値よシも大きくなシ、シャープに集光す
ることができなくなる。この状態を示したものが第５図
である。第５図において。Furthermore, when the parallel light u11 tilted with respect to the optical axis +41 shown in the Fresnel zone play (3) K shown in Fig. 1 is incident, comatic aberration occurs, and the spot diameter at the condensing point reaches the diffraction limit. If the value is too large, it will not be possible to focus the light sharply. FIG. 5 shows this state. In FIG.

（Ｉｌｌ　（Ｉｌａバ１１ｂ）は上記光軸（４）に対し
て傾きをもつ入射平光、（１２１（１２ａバ１２ｂ）　
ｆｉ入射平行光（１１１（ｌｌａバ１１ｂ）に対する出
射光、　（１３１は入射平行光ｕｉｌに対する集光点で
ある。フレネルゾーン（２）で回折された出射光ｕ２１
は上記境界（９）で屈折され集光点［３１に向う光線と
なるが、入射平行光叩の７レネルゾーンに対する入射高
さが、入射平光（Ｉｌｌと入射平行光（１１ａバ１１ｂ
）とでは異なるため、フレネルゾーン（２）で回折され
た出射光α２）と出射光（１２ａＪおよび出射光（１２
ｂＪは境界面（９）で屈折されたのちも１点では交わら
ず互いに異なる位置で交わる。(Ill (Ila bar 11b) is the incident flat light having an inclination with respect to the optical axis (4), (121 (12a bar 12b)
fi is the outgoing light for the incident parallel light (111 (lla bar 11b), (131 is the condensing point for the incident parallel light uil. The outgoing light u21 diffracted by the Fresnel zone (2)
is refracted at the boundary (9) and becomes a ray heading toward the condensing point [31, but the incident height of the incident parallel light to the 7 Renel zone is the same as the incident parallel light (Ill) and the incident parallel light (11a and 11b).
), the output light α2) and the output light (12aJ) diffracted at the Fresnel zone (2) and the output light (12aJ) are different from each other.
Even after being refracted at the boundary surface (9), bJ does not intersect at one point but intersects at different positions.

他の光線につＶても同じである。その差異はいわゆるコ
マ収差となって現われ集光点（１：１における像はボケ
、そのスポット径は回折限界による値よルも大きくなる
。第６図に、第５図の集光点（＋３１におけるスポット
ダイアグラムを示す。The same applies to other light rays. This difference appears as so-called comatic aberration, and the image at the focal point (1:1) is blurred, and the spot diameter also increases due to the diffraction limit. Figure 6 shows the focal point (+31 shows a spot diagram in .

このように、従来のフレネルゾーングレートでは、屈折
率が１よル大きい物質中でシャープに集光できないとい
う欠点があるとともに、入射平行光が光軸に対して傾く
とコマ収差を生じシャープに集光することはできないと
いう欠点があった。In this way, conventional Fresnel zone grates have the disadvantage of not being able to sharply focus light in a material with a refractive index greater than 1, and also cause coma aberration when incident parallel light is tilted with respect to the optical axis, making it difficult to focus sharply. The drawback was that it could not emit light.

この発明は９以上の欠点を除去するため、平凹レンズの
凹面側を平行光が入射する入射面とし。In order to eliminate the above defects, this invention uses the concave side of the plano-concave lens as the incident surface on which parallel light enters.

平面側に７レネルゾーンを作成し、正弦条件の不満足ｔ
が小さくなるようＫまた。屈折率が１以上の物質中で回
折限界のスポット径となるようにフレネルゾーンの輪帯
半径、上記平凹レンズの厚み。Create 7 Renel zones on the plane side and dissatisfy the sine condition t
K again so that it becomes smaller. The annular radius of the Fresnel zone and the thickness of the plano-concave lens so that the spot diameter is at the diffraction limit in a substance with a refractive index of 1 or more.

Ｍ折半および曲率半径等を決定し１球面状差を除去しか
つコマ収差が小さくなるよう例したものであシ、以下図
面について詳細に説明する。This is an example in which the M-fold, radius of curvature, etc. are determined, one spherical difference is removed, and comatic aberration is reduced.The drawings will be described in detail below.

オフ図は本発明の７レネルゾーンプレートの輪帯半径を
求めるための模式図である。このフレネルゾーングレー
トよシ距ＲＬｔのところＫある屈折率ｎ３≧１の透明物
質（８）中忙表面（９）よシ距Ｍｔのところで入射平行
光（５）を集光させかつコマ収差が小さくなるように７
レネルゾーンの輪帯半径１ｋ。The off-line diagram is a schematic diagram for determining the annular radius of the 7-Renel zone plate of the present invention. At the distance RLt from this Fresnel zone grating, a transparent material (8) with a certain refractive index n3≧1, a medium surface (9), and the incident parallel light (5) are condensed at the distance Mt, and the coma aberration is small. so that it becomes 7
The ring radius of the Renel zone is 1k.

平凹レンズの厚み、屈折率および曲率半径を求める。オ
フ図において、ｕ５）は平行透ＥＡ板、ｕ６）は凹面透
明板、　ｆｉｌは屈折光、　（１８１ｔ’ｉ屈折光、　
（１９１は平凹レンズ、（２Ｑｌ／ｒｉ基準平面である
。Find the thickness, refractive index, and radius of curvature of the plano-concave lens. In the off-line diagram, u5) is a parallel transparent EA plate, u6) is a concave transparent plate, fil is refracted light, (181t'i refracted light,
(191 is a plano-concave lens, (2Ql/ri reference plane.

オフ図において、入射平行光（５）を集光点Ｆで１点忙
集光するためＫは、基準平面上の点Ａから凹　−面透明
板上の点Ｂから平行透明板（１５１上の点Ｃと７レネル
ゾーン上の点りを蚤て、透明物質上の点Ｅで屈折して集
光点Ｆに至る光学距離と、基準平面上の点０から点Ｐと
点Ｑと点Ｒと点Ｓを予て点Ｆに至る光学距離との差が１
／２波長の整数倍になることである。In the off-line diagram, in order to condense the incident parallel light (5) to one point at the converging point F, K moves from point A on the reference plane to point B on the concave transparent plate to the parallel transparent plate (on the parallel transparent plate 151). The optical distance from points C and 7 on the Renel zone to the focal point F after refraction at point E on the transparent material, and from point 0 on the reference plane to point P, point Q, point R, and point The difference between S and the optical distance to point F is 1
/2 wavelength.

すなわち、この条件はオ（２）式 ％式％ ） のように書くことができる。ここで０１　　は上記凹面
透明板の屈折率＋　　０２は上記平行透明板の屈折率。That is, this condition can be written as (2). Here, 01 is the refractive index of the concave transparent plate + 02 is the refractive index of the parallel transparent plate.

ｋは輪帯の番号でに＝ＬＺ・・・、λは波長である。k is the number of the ring zone=LZ..., and λ is the wavelength.

次に１点Ｂと点Ｃお工び点Ｅで各光線が屈折することを
考慮し、角度Ｑ１とＱ２とＱ３とＱ４とＱ５と暢とをオ
フ図のようにとシ、かつ、上記凹面ガラス板の中心部の
厚さをｄ１曲率半径を’１＋平行ガラス板の厚さをｄ２
＋上牝フレネルゾーングレートと透明物質（８）との距
離をｔ、上記透明物質（８）の表面（９）よシ集光点ま
での距Ｍをｔとするとオ（２）式はオ（３）式のように
書ける。Next, considering that each ray is refracted at point B, point C, and point E, set the angles Q1, Q2, Q3, Q4, Q5, and the angles as shown in the off-line diagram. The thickness of the center of the glass plate is d1 The radius of curvature is '1 + The thickness of the parallel glass plate is d2
+Upper Female If the distance between the Fresnel zone grating and the transparent material (8) is t, and the distance M from the surface (9) of the transparent material (8) to the focal point is t, then Equation O(2) becomes O( 3) It can be written as Eq.

（ｆ　＋Ｊｄ１　＋ｎ２ｄ、Ｂ　＋ｔ＋ｎ３す＝に、−
・−・・・・・−・・・・・・・・・・・−・・・・・
・・・・・１３）また９点Ｂと点Ｃおよび点Ｅにおいて
はスネルの法則よシ ｆｉｌｎ＃１　＝ｎ１ａｌｒｌｌ’２　　・甲甲曲Ｕ―
山……ψ…・ｔ・・−・・旧・・・―…・・ｅ・・−（
４）ｎｌａｌｎ＃３　＝ｎ２ＮＩ’ｌθ４　・・―・・
−川・・・・・−・・・・・・…・・・・・・・甲・・
・・・・・・・・曲１５１ａｉｎθ５　＝ｎ３　＠ｌｎ
θ６・・φ・Φ・・・・Φ−・・−Φ・・・Φ・−・・
・φ−・ｅ・・ｅ−・−・・・―・・・・−・―Φ−１
・・・ｔ６１０３”’１−θ２　・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・・
・・・＋７１と書ける。(f +Jd1 +n2d, B +t+n3s=, -
・−・・・−・・・・・・・・・・・・・−・・・・・
...13) Also, at point 9 B, point C, and point E, according to Snell's law, filn#1 = n1alrll'2 ・Instep U-
Mountain……ψ…・t・・−・・old・・・・・・・・e・・−(
4) nlaln#3 =n2NI'lθ4...
−River・・−・・・・・・・・・・・・・・・・A・・
・・・・・・・・・Song 151ainθ5 =n3 @ln
θ6・・φ・Φ・・・・Φ−・・−Φ・・・Φ・−・・
・φ−・e・・e−・−・・・・・・・・−・−Φ−1
...t6103"'1-θ2 ......
・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・
...can be written as +71.

次に、フレネルゾーンの輪帯の半径をｒｋとすると。Next, let the radius of the Fresnel zone be rk.

ｒ　ｋ＝＝ＡｔａｍＱｓ　＋ｆｔａｍθ６＝ｒ　＊　ｉ
　ｎθ１＋（ｒ　（ｌ　　Ｃｏａｌ’　Ｉ　）十ｄ１ノ
ｔａｎθ３十ｄ２ｔａｎθ４・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・（８
）と書ける。r k==AtamQs +ftamθ6=r*i
nθ1+(r (l Coal' I) 10d1nottanθ30d2tanθ4・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・
・・・・・・・・・・・・・・・・・・・・・・・・(8
) can be written.

以上の第３式から第８式を０１から０６を変数とする連
立方程式として解き、その解を第８式に代入すると輪帯
の半径ｒｋが求ま９９球面収差が除去されたものとなっ
てｂる。Solving the above equations 3 to 8 as simultaneous equations with variables 01 to 06, and substituting the solution into equation 8, the radius rk of the annular zone is found and the 99 spherical aberration is removed. bl.

しかし、コマ収差を生じないためにはいやゆる正弦条件
を満足する必要があるが、必ずしもすべての入射光線に
対して正弦条件を満すようＫすることはできない。正弦
条件の不腐定量−２ｓ　、ｃ　。However, in order to prevent coma aberration from occurring, it is necessary to satisfy a sine condition, but it is not necessarily possible to set K so that the sine condition is satisfied for all incident light rays. Incorruption quantity for sine condition -2s,c.

と書ける。ここで［は焦点距離である。It can be written as Here, [ is the focal length.

本発明によるフレネルゾーンプレートでは、残葉コマ収
差の評価量として から０．６　の間で となるように凹面透明板の屈−１７？率ｎ１．厚さｄｌ
と曲率半値ｒおよび平行透明板の厚みｄ２　　と屈折率
ｎ２　の値を選択して連立方程式を解く。In the Fresnel zone plate according to the present invention, the curvature of the concave transparent plate is set such that the estimated amount of residual coma aberration is between -17 and 0.6. Rate n1. thickness dl
The simultaneous equations are solved by selecting the values of , the half value of curvature r, the thickness d2 of the parallel transparent plate, and the refractive index n2.

このように、フレネルゾーンの輪帯半径’ｋｅ上記凹面
透明板の厚みｄｌ　　と屈折率”Ｉｓ上記平行透明板の
厚みｄ２と屈折率ｎ２とをきめると、入射平行光が光軸
１４１　Ｋ対し頑いたとしても出射光のコマ収差は除去
されているので集光点（１３１ではシャープなスポット
が得られる。オ８因はこの状況を示したものであル、オ
９図は集光点（１３１におけるスポットを示したもので
ある。In this way, if we determine the annular radius of the Fresnel zone 'ke, the thickness dl of the concave transparent plate, the refractive index 'Is, the thickness d2 of the parallel transparent plate, and the refractive index n2, the incident parallel light will be rigidly aligned with respect to the optical axis 141K. Even if it is, the coma aberration of the emitted light has been removed, so a sharp spot can be obtained at the converging point (131). This shows the spots in .

第１０図の実線（インは残留コマ収差の評価書が２．８
２λであ）凹面透明板（１６）と平行透明板１５１の屈
折率が異なる場合の入射高さと正弦粂件不満足潰との関
係を示したものであシ、パラメータの値ヲ、ｎ１−１．
７．ｎ２．　＝＝　１．５　　ｎ３＝１．５．　ｊｌ　
”＝１　ｍｒ、　ｄ２　＝０．５　ｍｍ、　　Ｌ”＝　
２　ｗｎ、　　ｔ　＝　１．２ｍｍ　、λ＝０．７８．
ａｍ　とし開口数ＮＡを−０４５としたものである。The solid line in Figure 10 (in indicates the residual coma aberration evaluation report is 2.8).
2λ) This shows the relationship between the incident height and the unsatisfactory collapse of the sine wave condition when the refractive index of the concave transparent plate (16) and the parallel transparent plate 151 are different.The parameter values are n1-1.
7. n2. == 1.5 n3=1.5. jl
”=1 mr, d2=0.5 mm, L”=
2wn, t=1.2mm, λ=0.78.
am and the numerical aperture NA is -045.

図中９点線（口λは開口数と直径が同じな従来の７レネ
ルゾーングレートの収差を示したものであル。The 9-dotted line in the figure (the aperture λ indicates the aberration of a conventional 7-Lesnel zone grating with the same numerical aperture and diameter).

これにくらべて本発明によるフレネルゾーングレートの
コマ収差は非常忙小さくなっていることがわかる。In comparison, it can be seen that the comatic aberration of the Fresnel zone grating according to the present invention is extremely small.

第１１　図は凹面透明板（１６１と平行透明板Ｕ５＋の
屈折率を同じとし、上記凹面透明板（１６１と平行透明
板（１５１を分割せずＶＣＩ体とした残留コマ収差の評
価量が４．５５λとなる場合であるが、この場合でもコ
マ収差の発生は小さいことがわかる。FIG. 11 shows that the refractive index of the concave transparent plate (161) and the parallel transparent plate U5+ are the same, and the evaluation amount of residual coma aberration is 4. 55λ, and it can be seen that even in this case, the occurrence of comatic aberration is small.

第１２図は本発明の一実施例で６シ、平行透明板（］５
ｊの上に１輪帯の半径ｒＢ、・の０とｒｌとの間および
ｒ２に−１とｔ２ｋ（ｋ　”：’　１．２　”・）との
間および’ｚｋ　−１（！：　ｔ２１　（ｋ　；１．２
．・＝　）との間のみに屈折率がｎ（Ｎ１）の透明物質
１２１Ｊを付けてフレネルゾーン（２）を形成した位相
型のフレネルゾーングレートである。Figure 12 shows an embodiment of the present invention with 6 parallel transparent plates (]5
The radius of one ring zone on j is between 0 and rl of rB, · and between -1 and t2k (k '':' 1.2 '' ·) on r2 and 'zk -1 (!: t21 ( k; 1.2
．． This is a phase-type Fresnel zone grating in which a transparent material 121J with a refractive index of n (N1) is attached only between the .

また、第１３図は本発明の他の実施例であシ、平行透明
板ｕ５１の上に１輪帯の半径ｆｋのＯからｊ２およびｊ
２　からｒ２に＋２（ｋ　＝＝　１．２・・・）　の輪
帯の間では連続的に厚さが薄くなる屈折率ｎの透明物質
０２含付けて７レネルゾーンを形成しブレーズ化を計っ
た位相型のフレネルゾーンプレートである。FIG. 13 shows another embodiment of the present invention, in which one ring zone from O to j2 and j of radius fk is placed on a parallel transparent plate u51.
From 2 to r2, a transparent material 02 with a refractive index of n whose thickness becomes thinner continuously between the annular zones of +2 (k == 1.2...) was included to form a 7-Renel zone and blazed. It is a phase type Fresnel zone plate.

第１′４図は本発明の他の実施例であシ、凹面透明（１
６１と平行透明板（１５１とを同じ屈折率の透明板とし
。1'4 shows another embodiment of the present invention, which has a concave transparent surface (1
61 and a parallel transparent plate (151 are transparent plates with the same refractive index).

第１３図のように分割せずに１体の平凹レンズとしてそ
の平面側にフレネルゾーンを形成したものである。この
とき輪帯の半径ｒｋのｒ２に−ｓとｆ２ｋ　　（（ｋ＝
＝１．２．・・・Ｊとの間のみに屈折率がｎ　Ｃ’ｉ１
）の透明物質１２］）　全付けて７レネルゾーン（２）
を形成する。As shown in FIG. 13, this is a single plano-concave lens without being divided into parts, with a Fresnel zone formed on its plane side. At this time, −s and f2k ((k=
=1.2. ...The refractive index is n C'i1 only between J
) Transparent substance 12]) 7 Renel zones (2) with all attached
form.

第１５　図は本発明の他の実ＩＡ列であシ、第１４図の
７レネルゾーンｔ［−１３１ｇのフレネルゾーンと同様
にしてブレーズ化をＪｌｏりた構成としたものである。FIG. 15 shows another actual IA array according to the present invention, which has a configuration in which the blaze is reduced by Jlo in the same manner as the Fresnel zone of 7 Renel zone t [-131 g in FIG. 14.

オス２図、第１３図、第１４　　図および第１５　因に
示した本発明に係わるフレネルゾーングレートを用いれ
ば、入射平行光が上記フレネルシー３プレー　ト＋３１
の光軸（４）忙対して相対的に傾いたとしてもコマ収差
が小さいので回折限界して近いスポット径となるシャー
プな集光が得られる。If the Fresnel zone grates according to the present invention shown in Figures 2, 13, 14, and 15 are used, the incident parallel light will pass through the Fresnel Sea 3 plates + 31
Even if the optical axis (4) of the optical axis (4) is relatively tilted, the coma aberration is small, so sharp light condensation with a spot diameter close to the diffraction limit can be obtained.

なお９以上はフレネルゾーンを透明な物質（２１１を用
いて、その厚みを変えることによシ位相型の７レネルゾ
ーンを形成する場合について述べたが。9 and above describes the case where a transparent material (211) is used as the Fresnel zone and a phase-type 7 Fresnel zone is formed by changing its thickness.

輪帯箪径ｒｋ　の０とｆ］　の間およびｒ２にとｒ、　
２に＋１（ｋ＝１．　Ｚ−Ｊとの間を透明、ｒ２に−＋
とｒ２ｋ（ｋ＝１．２・・・〕との間を不透明にしたフ
レネルゾーンをｆ″Ｆ−製しても効率は上記位相型フレ
ネルゾーンにくらべて低下するが、同様の集光作用を行
うのでこのような構成としてもよい。between 0 and f of the annular diameter rk and between r2 and r,
+1 to 2 (k = 1. Transparent between Z-J, -+ to r2
Even if an opaque Fresnel zone is made between f''F and Therefore, such a configuration may be used.

以上のように、この発明に係るフレネルゾーンプレート
では、平凹レンズの凹面を平行光が入射する入射面とし
、平面側に７レネルゾーンを作成し、その輪帯の平径が
遅立方程式第３式からオ８式の解となるようＫＬ、かつ
残留コマ収差の評価量が小さくなるよ５に平凹レンズの
屈折率、厚みおよび曲率平径を決定することによシ、屈
折率が１以上の透明物質内で回折限界のスポット径およ
びコマ収差の発生量が小さくなるようにしたものであ勺
、入射平行光が光軸に対して傾いたとしても回折限界に
近いスポット径が得られ、シャープな集光特性が得られ
るという効果を有する。As described above, in the Fresnel zone plate according to the present invention, the concave surface of the plano-concave lens is used as the incident surface on which parallel light enters, seven Fresnel zones are created on the plane side, and the flat diameter of the ring zone is expressed by the third equation By determining the refractive index, thickness, and diameter of curvature of the plano-concave lens in 5 so that KL becomes the solution to Equation 8, and the evaluation amount of residual comatic aberration is small, This is a method that reduces the diffraction-limited spot diameter and the amount of coma aberration within the material.In addition, even if the incident parallel light is tilted with respect to the optical axis, a spot diameter close to the diffraction-limited spot diameter can be obtained, resulting in a sharp image. This has the effect of providing light condensing properties.

【図面の簡単な説明】[Brief explanation of the drawing]

牙１図は従来の７レネルゾーンプレートを用いて光軸に
平行な入射平行光を集光する場合の模式図、第２図は第
１図に対する集光点でのスポットを示す図、第３図は従
来のフレネルゾーングレートを用いてｎ＞１の透明物質
に集光する一場合の模式図、第４図は第３図に対する集
光点でのスポットを示す図、第５図は従来のフレネルゾ
ーンプレートを用いて光軸に対して傾いた入射平行光を
集光する場合の模式区、オ６図／Ｉ′ｉ第５図に対する
集光点でのスポットダイアグラム、オフ図は本発明に係
るフレネルシー７プレートの輪帯半径を求めるための模
式図、第８図は本発明に係るフレネルシー７グレートを
用いて光軸に対して傾いた入射平行光を集光する場合の
模式図、１９図は第８図に対する集光点でのスポットを
示す区、第１０図と第１１図はコマ収差曲線の例、第１
２図はこの発明に係るフレネルゾーングレートの一実施
例を示すψ図、第１３図はこの発明に係るフレネルゾー
ンフ。 レートの他の実施例を示す図、第１４図はこの発明に係
るフレネルゾーンプレートの他の実施例を示す図、第１
５図はこの発明に係るフレネルゾーンプレートの他の実
施例を示す図である。 図中、（１）はガラス板、（２）はワレネルゾーン、（
３）はフレネルゾーンプレート、＋４１は光軸、（５）
は入射平行光、（６）は出射光、（７）は集光点、（８
）は屈折率が１以上の透明物質、（９）は表面、叫は焦
点、ｕＤ（ｉａ）（１１ｂ）は入射平行光、　（１２１
（１２ａバ１２ｂ）は出射光、　（１３１は集光点、　
Ｑ４１は焦点、ｕ５）は平行透明板、ｕ６）は凹面透明
板、　＋１７１は屈折光、ａ８１は屈折光、　（１９］
は平凹レンズ。 （２１＋１は基準平面、Ｑｌ）は屈折率が１以上の透明
物質である。 なお１図中、同一あるｈＦｉ相当部分には同一符号を付
して示しである。 ネｒｆａ　　　　　ｌ 卑２　Ω 塾仝脇 Ｉ ネ　フ　１５イ）１ ＋ｔｏｒ’；ｈ 、５　ダ弧イ・イブ１　　　　　　　　　　　　　　　
　　　　　　　　　　　　　　　　　　　　　　　　　
　　　　　″）’ｌ、＋＋＋ハ　　　　　　　　　ネ１
２図（い 事１３　Ｑ ’４．＋４必 ネ１５島Figure 1 is a schematic diagram of a case where a conventional 7-Renel zone plate is used to condense incident parallel light parallel to the optical axis. Figure 2 is a diagram showing the spot at the focal point compared to Figure 1. Figure 3 is a schematic diagram of a case in which light is focused on a transparent material with n>1 using a conventional Fresnel zone grating, Figure 4 is a diagram showing the spot at the focal point compared to Figure 3, and Figure 5 is a diagram of the conventional Fresnel zone grating. A schematic diagram of the case where incident parallel light tilted to the optical axis is condensed using a Fresnel zone plate, a spot diagram at the condensing point for Fig. 6/I'i, and Fig. 5. FIG. 8 is a schematic diagram for determining the annular radius of the Fresnel Sea 7 plate according to the present invention, and FIG. , Figure 19 shows the spot at the focal point for Figure 8, Figures 10 and 11 are examples of coma aberration curves,
FIG. 2 is a ψ diagram showing an embodiment of the Fresnel zone grate according to the present invention, and FIG. 13 is a Fresnel zone grate according to the present invention. FIG. 14 is a diagram showing another embodiment of the Fresnel zone plate according to the present invention.
FIG. 5 is a diagram showing another embodiment of the Fresnel zone plate according to the present invention. In the figure, (1) is the glass plate, (2) is the Wallenel zone, (
3) is Fresnel zone plate, +41 is optical axis, (5)
is the incident parallel light, (6) is the output light, (7) is the focal point, (8
) is a transparent substance with a refractive index of 1 or more, (9) is the surface, yi is the focal point, uD(ia) (11b) is the incident parallel light, (121
(12a bar 12b) is the emitted light, (131 is the condensing point,
Q41 is the focus, u5) is the parallel transparent plate, u6) is the concave transparent plate, +171 is the refracted light, a81 is the refracted light, (19)
is a plano-concave lens. (21+1 is a reference plane, Ql) is a transparent substance with a refractive index of 1 or more. In FIG. 1, the same parts corresponding to hFi are indicated by the same reference numerals. nerfa l base 2 Ω school side I ne f 15 ii) 1 +tor';

″)'l, +++ Honey 1
Figure 2 (Igoto 13 Q'4.+4 must have 15 islands

Claims (1)

【特許請求の範囲】 ｉｌ）　　平行光を屈折率が１以上の透明物質中の１点
に集光させるフレネルゾーンプレートにおｈで。 屈折率がｎ２　　で厚さがｄ２　　である平行な透明板
と。 屈折率がｎ】で中心の厚さがｄｌで一方の側を半径ｔの
凹面とし、もう一方の側を平面とした形状をもつ凹面透
ＢＡ板の平面側に上記平行透明板とを張合せｆｃｍ成の
平凹レンズの凹面揃ヲ平行光が入射する側とし、上記平
凸レンズの平面ｆ目！Ｉ　Ｋフレネルゾーンを形成し、
かつ上記フレネルゾーン中によシに番目の＠帝半径ｆｋ
が０１と０２と０３と８４と０５と０６を変数とする連
立方程式 ％式％ （ここでｋ　＝　１．２．・・・、ｔはフレネルゾーン
グレートの出射側から屈Ｆｒ率ｎ３　の透明＃！：Ｊ質
の表面鷹での距離、ｔは上記透明物質の表面から集光点
までの距離、λは波長である） の解によシ ｒｋ＝ｌ−１ａｎθ５＋ｔｔａｎθ６ と与えられ、かつ上記フレネルゾーンプレートの開口数
Ｎ、Ａが０．１から０．６の範囲で残留コマ収差の絆価
敵が （ここでｋｍａｘ／ｒｉ最大輪帝数、ｆは焦点距離であ
るンとなるようにしたことを特徴とするフレネルゾーン
グレート。 （２）フレネルゾーンの輪帯半径１２に−１とｒｋ（ｋ
＝　１．２．・・・λとの間のみに屈折率がｎ（ｎ）１
ノの透明物質を付けたことを特徴とする特許請求の範囲
オｉ１１項記載の７レネルゾーンプレート（３）　　フ
レネルゾーンの輪帯半径ｒ１．の０からｆ２および１２
ｋからｒｚｋ十ｚ　（ｋ＝ｉ、　２・・・λの輪帯の間
では連続的に厚さが薄くなる屈折率ｎ（）ＩＪの透明物
質を形成しフレネルゾーンのブレーズ化を計ったことを
特徴とする特許請求の範囲オ山頂記載の７レネルゾーン
プレート （４）平凹レンズを１枚の透明板によ多形成したことを
特徴とする特許請求の範囲オ（２）項および第１３）項
記載のフレネルゾーンプレート[Claims] il) A Fresnel zone plate that focuses parallel light onto one point in a transparent material having a refractive index of 1 or more. Parallel transparent plates with a refractive index of n2 and a thickness of d2. The parallel transparent plate is laminated on the flat side of a concave transparent BA plate with a refractive index of n], a center thickness of dl, a concave surface with a radius of t on one side, and a flat surface on the other side. The concave surfaces of the fcm plano-concave lens are the parallel light incident side, and the plane of the plano-convex lens is the f-th plane! I K forms Fresnel zone,
And the second @ imperial radius fk in the above Fresnel zone
is a simultaneous equation with variables 01, 02, 03, 84, 05, and 06 (where k = 1.2..., t is a transparent # of refractive index n3 from the exit side of the Fresnel zone grating !: Distance in terms of the J-quality surface, t is the distance from the surface of the transparent material to the focal point, and λ is the wavelength). When the numerical aperture N and A of the plate are in the range of 0.1 to 0.6, the value of residual comatic aberration is set to be (where kmax/ri is the maximum ring coefficient, and f is the focal length. (2) −1 and rk(k
= 1.2. ...The refractive index is n(n)1 only between λ
7-Resnel zone plate (3) according to claim 11, characterized in that a transparent material is attached to the Fresnel zone ring radius r1. 0 to f2 and 12
A transparent material with a refractive index n()IJ that becomes thinner continuously between the annular zones from k to rzk1z (k = i, 2...λ) was formed, and the Fresnel zone was blazed. Claims O: 7-Renel zone plate (4) described on the summit of the mountain; Claims O: Claims O(2) and 13, characterized in that multiple plano-concave lenses are formed on one transparent plate. Fresnel zone plate described in )
JP264883A 1983-01-11 1983-01-11 Fresnel zone plate Granted JPS59127006A (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
JP264883A JPS59127006A (en) 1983-01-11 1983-01-11 Fresnel zone plate

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
JP264883A JPS59127006A (en) 1983-01-11 1983-01-11 Fresnel zone plate

Publications (2)

Publication Number Publication Date
JPS59127006A true JPS59127006A (en) 1984-07-21
JPS6311641B2 JPS6311641B2 (en) 1988-03-15

Family

ID=11535170

Family Applications (1)

Application Number Title Priority Date Filing Date
JP264883A Granted JPS59127006A (en) 1983-01-11 1983-01-11 Fresnel zone plate

Country Status (1)

Country Link
JP (1) JPS59127006A (en)

Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6269201A (en) * 1985-09-21 1987-03-30 Univ Osaka Irregular transmission type fresnel zone plate
JPH05210054A (en) * 1991-09-23 1993-08-20 Hughes Aircraft Co Dual eyepiece lens optical system using diffraction and refraction optical ele- ments
US5257133A (en) * 1991-09-11 1993-10-26 Hughes Aircraft Company Re-imaging optical system employing refractive and diffractive optical elements
US6865025B2 (en) * 2001-07-11 2005-03-08 Konica Minolta Opto, Inc. Aberration compensating optical element, optical system, optical pickup device, recorder and reproducer
CN114967127A (en) * 2022-06-16 2022-08-30 曹桂源 Design method of multi-wavelength achromatic ultrathin planar lens

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS6269201A (en) * 1985-09-21 1987-03-30 Univ Osaka Irregular transmission type fresnel zone plate
JPH0587801B2 (en) * 1985-09-21 1993-12-20 Oosaka Daigakucho
US5257133A (en) * 1991-09-11 1993-10-26 Hughes Aircraft Company Re-imaging optical system employing refractive and diffractive optical elements
JPH05210054A (en) * 1991-09-23 1993-08-20 Hughes Aircraft Co Dual eyepiece lens optical system using diffraction and refraction optical ele- ments
US6865025B2 (en) * 2001-07-11 2005-03-08 Konica Minolta Opto, Inc. Aberration compensating optical element, optical system, optical pickup device, recorder and reproducer
CN114967127A (en) * 2022-06-16 2022-08-30 曹桂源 Design method of multi-wavelength achromatic ultrathin planar lens
CN114967127B (en) * 2022-06-16 2023-09-12 曹桂源 Design method of multi-wavelength achromatic ultrathin planar lens

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